Hypothesis Testing

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Objective: Using hypothesis testing to compare the flying distance of the 2 catapults, by using data from different samples with the same number of tests.

DOE PRACTICAL TEAM MEMBERS (fill this according to your DOE practical):

1. Person A (Bjorn)

2. Person B (Darren)

3. Person C (Gwyn)

4. Person D (Cui Han)

5. Person E (Hai Jie)

 

 

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result)

:

 

Data collected for FRACTIONAL factorial design using CATAPULT B (fill this according to your DOE practical result):

Bjorn will use Run #1 from FRACTIONAL factorial and Run#1 from FULL factorial.

Darren will use Run #7 from FRACTIONAL factorial and Run#7 from FULL factorial.

Gwyn will use Run #6 from FRACTIONAL factorial and Run#6 from FULL factorial.

Cui Han will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.

Hai Jie will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

 

USE THIS TEMPLATE TABLE and fill all the blanks

The QUESTION	The catapult (the ones that were used in the DOE practical) manufacturer needs to determine the consistency of the products they have manufactured. Therefore they want to determine whether CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.
Scope of the test	The human factor is assumed to be negligible. Therefore different user will not have any effect on the flying distance of projectile.   Flying distance for catapult A and catapult B is collected using the factors below: Arm length = 27.5 cm Start angle = 25 degree Stop angle = 45 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0):   Catapult A and B produce the same flying distance of projectile. μA=μB     State the alternative hypothesis (H1):   Catapult A and B produce different flying distance of projectile. μA≠μB
Step 2: Formulate an analysis plan.	Sample size is 8<30 Therefore t-test will be used.     Since the sign of H1 is ≠ , a left/two/right tailed test is used.     Significance level (α) used in this test is 0.05
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: nA=8 x̄A=82.4 sA=3.29     State the mean and standard deviation of sample catapult B: nB=8 x̄B=77.9 sB=2.03       Compute the value of the test statistic (t):   SL:0.05, at A=0.025, t0.975, v=14, t=2.145
Step 4: Make a decision based on result	Type of test (check one only) 1. Left-tailed test: [ __ ]  Critical value tα = - ______ 2. Right-tailed test: [ __ ]  Critical value tα =  ______ 3. Two-tailed test: [ __ ]  Critical value tα/2 = ± 2.145   Use the t-distribution table to determine the critical value of tα or tα/2     Compare the values of test statistics, t, and critical value(s), tα or ± tα/2   Calculated t=3.08, from the chart, t=±2.145, t is not in the acceptable range Therefore Ho is rejected.
Conclusion that answer the initial question	Catapult A and B produce different flying distance of projectile.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	We all rejected the null hypothesis and this shows that the 2 catapults produce different flying distances even when the settings are the same.   From the comparison, it shows that the design of the catapult is very important, the quality of the catapult is not persistent throughout even if there is a minor difference. Even we used a different set of data, and the t values obtained were very different, but it produced the same trend, which is the 2 catapults produce different flying distances. Hence I can infer that for both full and factorial analysis, the same trend will be produced if the settings for both full and fractional are kept the same.

Reflection:

I think hypothesis testing is very useful when we want to compare the test results, and it can help us to determine the properties of similar products based on the sample data. I found it difficult to produce the null hypothesis at the beginning, but after several practices, it became easier and clearer to me. Also, we have very different values since different sets of data were used, but the overall trend is the same. It is also important to determine which test and which formula to use based on the hypothesis generated. so I think this method is very helpful in future projects.